"I am really proud of the way we played today but we are under no illusion that we will win the title," the New Zealand captain said. "We are treating every game as a knock-out game.
"I am sure if we play the way we are, we can win it. If things go our way, we can win it. But we are not looking too far ahead."
New Zealand was runners-up in the first two editions, losing to England in 2009 and to Australia in 2010.
Lanning admitted the Southern Stars were outplayed by New Zealand.
"It is obviously disappointing, but we never quite got into the game," the Australia captain said. "Once you get on the back foot, it is very difficult to recover.
"New Zealand outplayed us in this game. We just did not play well enough and New Zealand did."
The White Ferns complete group play against South Africa on Sunday morning.
